Assignment:
Gains from trade and their distribution. A country (Home) is populated with workers who produce either food (F) or clothing (C). There are 800 workers producing food and 600 producing clothing "these numbers are fixed in the short run. Each food worker produces 9 units of food and each clothing worker produces 3 units of clothing. Workers own the output they produce and can trade with other workers. All workersshare the same preferences over food and clothing represented by the utility function: U(DC, DF) =DC(DF)^2 Hint: Recall the property of Cobb-Douglas utility functions relating expenditure shares on both goods.
(a) What are the aggregate endowments of food and clothing in this economy?
(b) What is the autarky relative price of clothing to food?
(c) In autarky, how many units of food and clothing will be consumed by a clothing worker? By a food worker?
(d) There also exists another country (Foreign) that looks surprisingly like the Homecountry except that there are 1200 food workers and 600 clothing workers in thiscountry. These workers have different (lower) productivity levels: a food workercan produce only 3 unit of food while a clothing worker can only produce 6 unitsof clothing. The workers in Foreign share the same preferences as those in Home.
Answer questions (a), (b) and (c) for the Foreign economy in autarky.
(e) Compare the autarky consumption levels of workers in both countries. What explains the differences between countries?
(f) Now assume that these 2 countries open to trade with each other.
(i) What will be the free trade relative price of clothing to food?
(ii) Describe the pattern of trade (which country exports what and how much). Verify that the export supply matches the import demand for both goods.
(iii) Calculate the new consumption levels of both types of workers in both countries.
(iv) For each type of worker in both countries, assess whether they are better offi in the new trade equilibrium. Could you have predicted this pattern beforecalculating the new consumption levels and the free trade price equilibrium? How?
(v) Now assume that all workers belong to representative families each containing 2 food workers and 2 clothing worker. Describe how the consumption patterns (the number of units of food and clothing consumed) of the families change between autarky and the trade equilibrium. Are the families in both countries unambiguously better off? Why should you not be surprised by this result?
(g) Without redoing the calculations in (f), describe how your answers would change if the productivity of both types of Foreign workers were multiplied by 10. In particular, what will happen to:
(i) The pattern of trade (what good is exported by each country)
(ii) The distribution of the gains from trade Which workers will gain from trade? What will happen to the families of workers in each country?
(h) Return to the trade equilibrium described in (f). If workers can switch occupations in the long run, what will happen to the number of workers in each industry (only describe the direction "not the magnitude" of the change)?